"""
Ordinary Least Squares Regression (OLSR):

Ordinary Least Squares Regression (OLSR) is a statistical method for
estimating the parameters of a linear regression model.
It is the most commonly used regression method,
and it is based on the principle of minimizing
the sum of the squared residuals.

Below is a simple implementation of OLSR
without using any external libraries.

WIKI: https://en.wikipedia.org/wiki/Ordinary_least_squares
"""

import numpy as np


def ols_regression(x_point: np.ndarray, y_point: np.ndarray) -> tuple:
    """
    Performs Ordinary Least Squares Regression (OLSR) on the given data.

    Args:
        x: The independent variable.
        y: The dependent variable.

    Returns:
        a (float): The intercept of the regression line.
        b (float): The slope of the regression line.

    Examples:
    >>> x = np.array([1, 2, 3, 4, 5])
    >>> y = np.array([2, 4, 6, 8, 10])
    >>> a, b = ols_regression(x, y)
    >>> float(a)  # Intercept should be 0.0
    0.0
    >>> float(round(b, 2))  # Slope should be 2.0
    2.0
    """

    # Calculate the mean of the independent variable and
    # the dependent variable.
    x_mean = np.mean(x_point)
    y_mean = np.mean(y_point)

    # Calculate the slope of the regression line.
    slope = np.sum((x_point - x_mean) * (y_point - y_mean)) / np.sum(
        (x_point - x_mean) ** 2
    )

    # Calculate the intercept of the regression line.
    intercept = y_mean - slope * x_mean

    return intercept, slope


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    # Load the data
    x_points = np.array([1, 2, 3, 4, 5])
    y_points = np.array([2, 4, 6, 8, 10])

    # Perform OLS regression
    intercept, slope = ols_regression(x_points, y_points)

    # Intercept (a) and slope (b) of the regression line
    print("Intercept:", intercept)
    print("Slope:", slope)

    # Predict the target variable for a new data point with
    # an independent variable value of 6
    x_new = 6

    # Make a prediction
    y_pred = intercept + slope * x_new

    print("Prediction:", y_pred)